I do not know what "vd" is or "k" or "l". From basics, your max current is 10,000/110 ~90 Amps. So you need a cable that can carry 90 A from source to load without dropping too much voltage down it. The voltage drop is normally 2.5%. This then defines the resistance of the cable R = (2.5/100) X (110/90) = .030 ohms. If you now look at the charts for cable you need to find a cable that is long enough for your needs that has a resistance equal or less then this value. Note the cable drops voltage down its live AND neutral conductors, so you need to work on .015 ohms for a single run.
Frank